Systematic design of drug delivery therapies
Introduction
An increasing number of people are affected by neurodegenerative diseases of the central nervous system (CNS) such as Parkinson's, Alzheimer's and Huntington's disease (NIH, 2007). Development of more efficient therapies for diseases of the CNS is hampered by difficulties related to administering therapeutic agents to the affected areas deep inside the brain. Many of the larger proteins with promising pharmacological potency in vitro cannot pass the blood brain barrier (BBB), thus never reaching the cells they are targeted to remedy. Direct injection of the drugs via catheters into the region of interest in the brain can effectively by-pass the BBB, and the penetration depths can be enhanced by convection (Morrison, Laske, Bobo, Oldfield, & Dedrick, 1994). This technique imposes a convective bulk flow field in the extracellular space of the porous brain tissues, thus carrying the drug deep into the brain.
Molecular transport properties of new drugs are usually studied by animal experiments. The interpretation of three-dimensional drug distribution data inside the tissues of rats, rabbits or sheep is not amenable to simplistic lumped or one-dimensional mathematical models. Moreover, the enormous size differences between the human and animal brains make the scaling of drug delivery modalities a non-trivial task. Therefore, there exists a need to create a systematic data-driven approach for the effective design of invasive drug delivery therapies that takes into account the geometric, physiological and biochemical complexity of brain–drug interactions.
Novel analytical imaging techniques such as MRI, functional MRI (fMRI), diffusion tensor imaging (DTI), computer tomography (CT) and positron emission tomography (PET) have improved medical diagnosis. However, the existing imaging technologies are serving physicians only in a qualitative sense. Quantitative information such as transport or metabolic reaction properties are typically not derived from images directly. There appears to exist a gap between high quality of imaging data and their use in quantitative analysis. In order to address the open challenges in accurately predicting drug distribution, its metabolic reaction rates and drug clearance through the blood, a new computational approach integrating clinical imaging data with first principles transport equations is presented. The proposed computer aided design methodology depicted in Fig. 1 aims at overcoming three major challenges. The first issue addresses the accurate reconstruction of the three-dimensional brain geometry. A process to seamlessly integrate imaging data with state-of-the-art geometric image reconstruction tools is presented. The second issue concerns the lack of physical and chemical properties such as diffusivity and metabolic uptake for novel drugs. A computational method for the accurate determination of transport and reaction properties from in vivo medical images with novel mathematical programming techniques called transport and kinetic inversion problem (TKIP) will be introduced. The TKIP will be illustrated via a simplified case study for dopamine kinetics. Finally, drug transport and metabolic rate coefficients will be used to determine optimal parameters for drug administration. These design parameters include: optimal placement and orientation of the injection catheter, catheter dimensions, and the number of drug release openings.
Section 2 describes the approach for the accurate reconstruction of the brain anatomy from images. Section 3 introduces the TKIP approach for the estimation of unknown parameters like diffusivity and kinetic reaction rates. Section 4 describes the finite volume method using generalized curvilinear coordinates for unstructured computational grids. Section 5 quantifies the distribution of a trophic factor and the intravenous injection of L-dopa in different regions of the human brain.
Section snippets
Capturing the complex brain geometry
Quantification of transport processes requires accurate reconstruction of the complex brain anatomy. Brain dimensions and physiological differences from subject to subject justify a patient-specific approach. Fig. 2a shows the brain's inner structure as seen in a histological image (Warner, 2001). Fig. 2b displays the reconstructed two-dimensional computational mesh.
This two-dimensional brain model is composed of volumes and boundary surfaces reconstructed from digital images using image
Discovery of unknown transport properties and metabolic rates
The stages of the computer assisted brain analysis methodology are depicted in Fig. 1. The brain geometry reconstruction was discussed above. The solution of the inversion problem using the finite volume method with the sensitivity equations is described next. We propose a computational method to accurately quantify unknown transport drug properties by interpreting concentration profiles displayed by advanced imaging techniques. Experimental measurements of drug concentration or fluid flow
Finite volume method for unstructured computational meshes
The finite volume method (FVM) aims to discretize partial differential equations (PDE) for species concentration and momentum expressed in Eqs. (2) and (3). In contrast to existing solution methods based on fixed point iterations, e.g. Simple algorithm (Patankar, 1980), we use finite volume discretization for direct and explicit evaluation of the transport equations appearing as equality constraints in the inversion problem. The proposed finite volume method is based on the transport of field
Quantitative analysis and design of drug administration
In this section, two drug administration techniques are discussed to illustrate the computer assisted drug therapy. The first example is the intravenous injection of L-dopa, a precursor to dopamine. The intraparenchymal administration of a trophic factor with a molecular weight of 30,100 kg/kmole is described as a second example for targeted drug delivery to the midbrain.
Conclusions
A systematic approach for the design of drug delivery policies has been introduced. It provides insight in the selection of parameters for drug therapies. The novel method consisted of three steps: (i) accurate reconstruction of the brain geometry, (ii) determination of unknown transport and kinetic properties from experimental data, and (iii) prediction of volumes of distribution. Two drug administration techniques were described, intraparenchymal injection of the nerve growth factor and
Acknowledgments
The authors would like to thank Materialise Inc. for providing a trial research license of Mimics image reconstruction software. The Fluent Inc. is acknowledged for supporting the initial phases of the research with trial Fluent and Gambit licenses. Financial support from the Sussman and Asher Foundation is gratefully acknowledged. Megan Mekarski's contributions during her summer REU project were supported by REU supplementary grants from NSF-EEC 0502272 and NSF-DMI 0328134.
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